Wednesday, August 13, 2003

The Two Cultures, and the Mathematization of Economics

Here's something to ponder for those intellectuals who, like J.K. Galbraith, decry the ever increasing mathematical sophistication required to keep up with the economics literature:

"Being denied a sufficiently secure experimental base, economic theory has to adhere to the rules of logical discourse and must renounce the facility of internal inconsistency. A deductive structure that tolerates a contradiction does so under the penalty of being useless since any statement can be derived flawlessly and immediately from that contradiction. In its mathematical form, economic theory is open to an efficient scrutiny for logical errors."

(Gerard Debreu, "The Mathematization of Economic Theory", American Economic Review, 1991)

The very rationale for axiomatizing economics likely provides the motivation for the complaints so often heard about the 'Bourbakization' of economic theory - the more clearly one has to lay out one's assumptions, and the more logically rigorous one's arguments have to be, the less room there is to steer the argument, by sleight of hand, in the direction one would like it to go.